Problem: Express this quotient in scientific notation: ${\frac{1.560\times 10^{-2}} {6.0\times 10^{-3}}}$
Explanation: Start by collecting like terms together. $= {\frac{1.560} {6.0}} \times{\frac{10^{-2}} {10^{-3}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.26 \times 10^{-2\,-\,-3}$ $= 0.26 \times 10^{1}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.26$ is the same as $2.60 \div 10$ , or $2.60 \times 10^{-1}$ $ = {2.60 \times 10^{-1}} \times 10^{1} $ $= 2.60\times 10^{0}$